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Four-quadrant flyback converter for direct audio power amplification

Ljusev, Petar; Andersen, Michael Andreas E.

Published in:11th European Conference on Power Electronics and Applications

Link to article, DOI:10.1109/EPE.2005.219419

Publication date:2005

Document VersionPublisher's PDF, also known as Version of record

Link back to DTU Orbit

Citation (APA):Ljusev, P., & Andersen, M. A. E. (2005). Four-quadrant flyback converter for direct audio power amplification. In11th European Conference on Power Electronics and Applications IEEE.https://doi.org/10.1109/EPE.2005.219419

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Four-quadrant flyback converter for direct audio power amplification

Petar Ljusev and Michael A.E. Andersen0RSTED * DTU AUTOMATION, TECHNICAL UNIVERSITY OF DENMARK

Elektrovej DTU Building 325Kgs. Lyngby DK-2800, Denmark

Tel: +45 4525 3486, Fax: +45 4588 6111E-mail: pl@oersted.dtu.dk, ma@oersted.dtu.dk

AcknowledgmentsThe SICAM project is funded under the grant of the Danish Energy Authority EFP no. 1273/02-0001and is performed in cooperation with Bang & Olufsen ICEpower a/s in Kgs. Lyngby, Denmark.

KeywordsConverter circuit, High frequency power converter, Switched-mode power supply

AbstractThis paper presents a bidirectional, four-quadrant flyback converter for use in direct audio poweramplification. When compared to the standard Class-D switching-mode audio power amplifier withseparate power supply, the proposed four-quadrant flyback converter provides simple and compactsolution with high efficiency. higher level of integration, lower component count. less board spaceand eventually lower cost. Both peak and average current-mode control for use with 4Q flybackpower converters are described and compared. lntegrated magnetics is presented which simplifies theconstruction of the auxiliary power supplies for control biasing and isolated gate drives. The feasibilityof the approach is proven on audio power amplifier prototype for subwoofer applications.

IntroductionIn parallel with the perfonnance improvement of the power electronics components in temns ofhigher power levels and switching speeds, new challenging application areas start to appear forthe switching-mode power conversion. One of them is certainly the audio power amplification,where the switching-mode Class D audio power amplifiers become increasingly popular dueto their efficiency, low losses, reduced volume and board space, with subsequent decrease inthe product cost. This application area was ruled by the linear electronics amplifiers for manydecades, but today they are leaving the scene since their poor efficiency and huge powerlosses are becoming major obstacle towards the trend of high-level product integration. ClassD amplifiers are not without pitfalls either, since they are especially prone to EMC problems.However, the early success of the switching-mode audio power conversion on the markettoday shows that the Class D amplifiers are an emerging technology with a bright future.

One of the usually overseen benefits of tie switching mode audio power conversion is tiepossibility of closely interconnecting the front-end switching-mode power supply and theClass D amplifier into a single integrated stage, since the switches in both aforementionedparts perform similar functions of power processing through switching and can be thereforemultiplexed. This results in a highly integrated product with simplified power supply and nointermediate DC-bus, reduced component count, smaller volume, shrunk power conversionchain and even higher efficiency, which is sometimes referred as SICAM - Slngle Conversion

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TR& IND 9D, 2Power supply

High bandwidth B|

Tracing powersupply X;

Bidirectional capabanity T ,1 T24

Direct audio power ampEfier t E

Fig. 1 SICAM roadmnap Fig, 2 Two-switch 4Q flyback SICAM

stage AMplifier [1]f[2]. It is also quite appealing for the Active Transducer (AT) [3] approachfor direct conversion of the mains power into acoustic output in one siinplified topologicalstage, like in the active loudspeaker systems and dedicated subwoofer units. Obviously, thesesimplifications are complicating the control design and coine on expense of slightly loweraudio performance, but are nonetheless representing an interesting alternative. Since the prinemover in the low-end segment of the market is the product price, direct audio power amplifiersi.e. SICAMs are rather challenging to investigate as a possible way of cutting the costs.

Four-quadrant flyback SICAMTopology and operation principles

The simplest way of developing direct audio conversion topologies is starting with a particularpower supply scheme and extending its capabilities 1. Firstly, the power supply controlbandwidth is increased over the intended power bandwidth i.e. over the highest frequencyof the signal that is to be amplified, resulting in tracling power supply with variable DCoutput voltage. This is usually done by decreasing the size of the output lowpass filter so thatits frequency response is flat over all the frequencies of interest and then drops rapidly toattenuate the switching harmonics. In order to complete the construction of the direct audiopower amplifier, bidirectional power flow capability is added to the tracking power supply byreplacing all the unidirectional components (for example, the secondary-side rectifiers) withbidirectional switches that can block voltage of either polarity and conduct current of eitherdirection (for example, two series MOSFETs with common source connection).Flyback converter presents the simnplest isolated power supply topology, where the filtering in-ductor is actually integrated into the isolation transformuer and represents neans of transfetringthe energy from the primary-side voltage source to the secondary-side load. Consequently, theflyback converter saves the designer one nagnetic component, but it increases the size and thestress exerted upon the other comnponents, like the output capacitor that is to supply the wholeload current for the periods wlhen the main switch is turned on. On the other hand, there isjust single-order filtering of the current switching harmonics at the output, performed solelyby the output capacitoi; which leads to substantial voltage ripple on the output. Therefore thistopology is used only at lower power levels, when its benefits are most pronounced.The two-switch four-quadrant (4Q) flyback SICAM is shown in Fig. 2. It is derived fromthe two-switch flyback converter, where the secondary side consists of two windings and twobidirectional switches: I!,1- T22 with parasitic diodes D21 D22 and T23 - T24 with parasiticdiodes D23 - D24. The primary side stays essentially the same,

The amplifier is operated in a way that the primary side switches are turned on until enoughenergy has been stored in the magnetizing inductance of the flyback transformer, which is

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Fig. 3 Waveforms of the 4Q flyback SICAM

afterwards released either through T21 -T22 or T23- T24 to charge the output capacitor to tdedesired voltage across the load. When the energy has been delivered to the load the currentis allowed to reverse so that part of the capacitor charge is delivered back to the magnetizinginductance and returned to the pnmary side during the on-tine of the main switches. Thisallows the flyback converter to operate in continuous conduction mode like a "rocking chair",where first the energy is delivered to the load side and then maybe it is partly returned backto the primary side. Some of the 4Q flyback waveforms are given in Fig. 3.The 4Q flyback SICAM can be constructed as either single-switch or two-switch. In thepractical implementations of single-switch DC-DC flyback converters, it is necessary to use aclamp on the primary side of the transformer to dissipate the energy stored in the primary-sideleakage inductance. However, the voltage across the transformer during the off-time of themain switch can have either polarity and therefore the primary side clamp can be chargedfrom the load side whenever the output voltage reflected to the primary side is higher than theclamp voltage. The two-switch 4Q flyback SICAM does not experience the same problem,since the transformer primary side during the off-time of the main switch is clamped tothe rectified input voltage by using the two freewheeling diodes Di, and D12. This voltageis always bigger than the reflected load voltage since it is lirnited by the design i.e. theduty cycle is less than 50%. Because of the same reason, the primary side switches do notneed to have bidirectional voltage blocking capability, but innust have bidirectional currentcapability (ex. MOSFETs) to allow continuous curTent mode operation. Taking into accountthe additional benefit that the two-switch flyback converter requires switches with just halfthe voltage blocking capability of the one-switch flyback converter, it can be concluded thatthe two-switch topology represents a very feasible choice for bidirectional converters fromcost and implementation perspective.The disadvantages of the flyback converter with regard to the large output capacitance neededfor filtering the switching hamnonics of the inductor current become even more pronouncedin its bidirectional implementation. The output capacitor is supplying the whole load currentduring the on-period of the main switches, therefore the demands set upon it are very stringent.Due to the bipolar nature of the output voltage, the unipolar alumniaium electrolytic typecapacitors found in conventional switching-mode power supplies cannot be used and the sizeof the output section is inevitably increased. Therefore, the flyback topology for SICAMs islimited to low power levels.

ISBN 90-I71S08-O

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The most difficult part of the design of the 4Q flyback SICAM power section is the selectionof the output capacitor and the flyback transfonner magnetizing inductance. The minimumoutput capacitor is determined by the desired maximum output voltage ripple:

cm = Q __ Io,maxDmaxAl.,max Al½fa(fs

where 0-,m,ax is the maximum load curTent, Dmax is the maximum duty cycle, AU4ax is themaximum voltage ripple and f3 is the switching frequency.Although Cmin is the minimum output capacitance needed with regard to the output voltageripple limit, it is also the optimal since increasing that value significantly over Cmin willresult in slower response. It will be shown in the next section that the actual output voltageripple can also depend on the bandwidth of the outer voltage loop.Choosing the optimal value of the inductance represents slightly greater challenge. One wayof choosing the magnetizing inductance is by determining the maximum slope of the averageoutput current i0 = I,sili(27wft) and associated average inductor current iL = i,1(l-D):

,51,max = 27TfmaxIo cos(27wfmaxt) t=o = 27wfmaxzIoS sIo.up-t(2-U,max - 1Drn2

and choosing the instantaneous rising slope of the inductor current X4/L to be at least 20times higher than the average inductor current slope SIL.max.The other possibility for selecting the magnetizing inductance is by noting that it is limitingthe minimum frequency of the nght-half plane zero fRrp_z [4]:

fRHPZ,min = Dm.iR _ 0.5 R (3)2irDaxma 27irLmaxIt is known that the maximum usable control bandwidth of a system is limited to approximatelyone third of the frequency of the tight half-plane zero [5] and one tenth of the switchingfrequency f,. This leads for example to the following selection rule:

Lmnax - 0o5 R -0.5 R (4)27w fRHPZ,min 27w 0.3f,Slightly different 4Q flyback converter has been presented in [6], where it is built around adedicated cffipset for ring generators. Its operation principles differ from the proposed simplesolution, since during the off-time of the main switch, the secondary side switches are operatedin a PWM manner and energy is transferred to the primary side via a separate winding withseries rectifier. Another difference is that the secondary side switches can block both voltagepolarities, but the current can only be unidirectional and the flyback converter operates indiscontinuous conduction mode without the aforementioned "rocking chair" effect.

Control of 4Q flyback SICAM

The selection of the control algorithm for the 4Q flyback SICAM represents a trade-off amnongmany different objectives, like stability, low distortion and simplicity of implementation.The simplest way of control is single loop output voltage control, where the only feedback istaken from the load voltage and is used afterwards to derive the main switch duty cycle. Themain disadvantages with this approach are the involved second order transfer function withthe continuous mode operation, which makes it very difficult to make satisfactory controlsynthesis, as well as the inability to correct for input line perturbations until changes areobserved in the output voltage.

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Much better performance can be achieved with current mode control, where the inner currentloop and the outer voltage loop are simultaneously used to derive the duty cycle of themain switch. While the voltage loop is always taken from the load, the selection of currentfor closing the inner current loop can ask for careful consideration. In the buck derivedtopologies, where the second order LC output filter is placed across the load, the inductorcurrent is essentially the load current and by controlling directly the inductor current, thedynamics of the load current is being governed too. On the other hand, the flyback outputcurrent is different than the inductor curTent by a factor which depends on the duty cycleand it can be disputed which of these two is to be controlled. However, if the goal of thecurrent selection is to simplify the control synthesis of the outer voltage loop, then obviouslycontrolling the inductor current helps move the pole associated with the inductor to higherfrequencies. Even more, sensing inductor current is sometimes easier due to its continuityand can be done in many different ways, some being more simple than the others. Therefore,in the following sections will be dealt only with inductor current control in the inner loop.There are many different ways to implement current mode control, among which the peak andaverage current mode control are probably the most applicable ones. They have some distinctadvantages and pitfalls, which define their specific application areas. They can be both usedin 4Q flyback SICAMs and their implementation is subject of the next few sections.

Peak current mode control

The block scheme of the control section of the 4Q flyback SICAM with peak current-modecontrol is given in Fig. 4. As shown, it is a cascade system where the inner loop sets theinductor current and the outer loop controls the output voltage. The absolute value of thecontrol voltage v0 gives the reference current iref, while its sign given by the comparatori.e. 1-bit quantizer Q determines which secondary-side bidirectional switch will be turned onduring the off-time of the primary side switches. The reference current ircf is subsequentlycompared with the instantaneous value of the switch current to determine the switching-offinstant, resulting in peak current mode control. Beside the aforementioned simplification of thetransfer function, the peak current mode control yields a simple solution with fast response,high rejection ratio of the input voltage perturbations and cycle-by-cycle current limiting.In order to avoid output voltage zero-crossing distortion, there must be some minimuminductor current delivered to the output even at idle. During this idling time, the 1-bit quantizer

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1~ 're.

D,~~~~~~~~~~~~~~~~~I

C, T- Vg~~~~~~~~~~~~~o Ton

stable unstable

Fig. 4 Peak current-m-ode control Fig. 5 Slope miatching

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is likely to be stuck in a certain state of the output stage, which means that the output voltagewill continue to increase in one direction. With other words, 4Q flyback SICAM does nothave any stable equilibrium state corresponding to idle, which represents a strong contrastto the conventional Class D audio power amplifier, where the duty cycle of 50% assureszero average output voltage with certain predetermined output filter ripple. In the 4Q flybackSICAM it is up to the outer voltage loop to sense this excessive voltage ripple and prohibit itby changing the sign of the control voltage v, and the associated output stage state. Therefore,in this implementation it is very important to have shorter time delays within the control loopand provide high control bandwidth, by increasing the gain of the phase compensator GV(S).The highest possible gain of the compensator at the switching frequency, which does notcause instability is determined by matching the up-slope of the increasing inductor currentand the down-slope of the falling output voltage, like shown in Fig. 5:

RsL = RC (5)Amax Rcs - cRi;C.v(5m)~4max L VTmax

wherc Rcs is the current sense resistor, V. is the DC source voltage, R is the load resistanceand A is the gain from the output voltage to the input of the current controller at f3.Design of the phase compensator GV(s) is performed by shaping the overall loop transferfunction L so that both sufficient gain throughout the desired signal frequency range andhigh bandwidth are obtained. The plotting of the loop transfer function is alleviated byassuming that the inner current loop operates ideally and the inductor culTent iL is followingthe reference current iref with a high degree of accuracy, although this essentially dependson the level of inductor current ripple AiL. The loop gain L and its constitutive palts are:

L(s) = Gv(s)Gitc(s)Gc,jt (s)Gopto(s)II1v(s)

GV(S) = K(1 + )

GiLC(S) 17CIC 6nRcsKcs ~~~~~~~~~~~~~~~~(6)0@iL (S) = RGI.sRCGCPtO(s) = Kfi

HV (s) 1

where the meaning of the corresponding transfer functions is given in Fig. 6.It is interesting to note that, although the 4Q flyback converter has much simpler powersection than the Class D amplifier with separate power supply, the control section shown inFig. 4 tends to be involved and is further aggravated by the need for crossing the isolationbarrier. The way this is usually done in a conventional flyback SMPS is to transfer thecurrent reference using a simple optocoupler, which often has a highly nonlinear currenttransfer ratio (CTR) when looked in a large signal sense. On the other hand, the operationof a 4Q flyback SICAM involves largely varying control signals and the current referenceiref must be transferred to the isolated primary side with high degree of accuracy to avoidexcessive distortion. The easiest way to do that is to use a linear optocoupler with servo loopbuilt around it for linearizing its CTR. This results in a combined primary and secondaryside control, where the phase compensator of the outer voltage loop resides on the secondary

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Primary side

Voltage Lim optocoupler Curent loop Outpuyt LPFcopensator

Voltage feedback

Fig. 6 Peak current mode control block diagram

side and the phase compensator of the inner current loop is implemented on the primary sidetogether with the sensing of the switch current. As an option, switch current can be sensedand transferred to the secondary side with a current transformer, so that all the control islocated on the secondary side. However, the gate drive signals for the primary side switchesstill need to be transferred back with a separate pulse transformer, thus complicating thisoption even further.

Average current-mode control

Beside the aforementioned advantages of the peak current-mode control with regard to itssimplicity, speed and cycle-be-cycle current limiting, there are also some serious drawbacks.The most important drawback is the fact that controlling the peak value of the inductorcurrent does not necessarily mean that the average inductor current value follows the currentreference, which becomes especially pronounced in the continuous mode operation with largeripple current and even more in the discontinuous mode. For example, if the peak inductorcurrent follows perfectly the sinewave current reference of the audio amplifier, the actualaverage inductor current is likely to be much different than the reference, depending on theamount of current ripple. As a side effect of this problen, the low frequency gain of the peakcurrent mode controller is limited and does not guarantee high performance throughout thewhole power bandwidth.Operation of the 4Q flyback SICAM with large inductor ripple current is desired for at leasttwo reasons. Firstly, large ripple is a result of low flyback transformer inductance whichallows for much smaller size of the magnetics. On the other hand, low inductance is alsoa must, since for proper operation of the audio power amplifier the current level must bechanged sufficiently fast to achieve the desired dynamics of the converter, This means thatcorrect control of the average inductor current with low distortion will be nearly impossiblewith peak current mode control,In order to reduce the distortion, average current mode control can be implemented andoptimized by slope matching for achieving optimal speed of the response [7], comparable topeak current mode control. By proper design of the phase compensator in the inner currentloop, sufficient gain can be provided even at low frequencies where peak current mode controlis unable to deliver the same perfornance when large inductor current ripple is present.Average current mode control also enables use of non-dissipative techniques for inductor cur-rent sensing, in contrast to the usual current sense resistor technique. The inductor current canbe estimated by putting additional winding on the flyback transformer and ideally integratingthe transformer voltage with electronic components. In this case all the control can be doneon the secondary side, and it is just the main switches gate drive that needs to be transferredto the primary side. In practice, integration of the transformer voltage is impossible due to

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hour-quadrant flybackconxcrtcr fordircet audio power ainplilicaeion ANL)ERSLN Michael

Fig. 7 Average current mode control block diagram

Fig. 8 Average current-mode control Fig. 9 Integrated magnetics

the non-zero offset of operational anplifiers, and what is usually done is low pass filteringto derive exactly the high frequency content of the inductor current. This essentially ineansthat the DC value of the inductor current with this method can not be recovered. Thus thelow frequency performance of the control circuit is left to the outer voltage loop. The controlblock diagram of the 4Q flyback SICAM with average current mode control is given in Fig. 7and the comnplete schematic is given in Fig. 8. Inductor current estimnator transfer function is:

G t($S) e * 1 (7)N , I

where 11.es and Ti-est represent the estimator gain and time constant, and and N' are theestinator and inductor numnber of turns respectively.

Integrated magnetics for 4Q flyback SICAMThe 4Q flyback SICAM belongs to the group of SICAMs with mnodulated transformer volt-ages, which ineans that the power flow th-ough the main winding of the power transformierdepends on the amplitude of the signal being reproduced. This approach does not allow forcontinuous and constant power flow to the auxiliary power supplies for control biasing andisolated gate drive of the secondary side bidirectional switches.

Although the aforeinentioned problem can be alleviated by using separate mains transformersor smnall isolated SMPSs for providing the auxiliary voltages, mnuch mnore elegant solutioncan be achieved through integrated magnetics, like shown in Fig. 9. The auxiliary half-bridgeconverter consisting from switches T13, T14 and capacitors C13, CL4 applies HF voltage on the

LOB 2005 - I2're.dcnItS

I-our-qu,Wnutt fIvIxtek converter for dirwt audio pcower,,unplificadoa ANE3- Mila

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two in series connected identical auxiliary windings on the outer legs of the main transformer.The flux created from both of them is the same and flows entirely in the outer legs, whilethe electromotive forces created by the center leg flux are equal and ideally cancel each otherin the auxiliary windings. Thus the two magnetic structures on the same core are completelyindependent in their operation. Two series connected auxiliary windings on the secondaryside are used to derive all the auxiliary voltages, operating as a DC transformer for simplicityor with variable duty cycle in some kind of standard SMPS configuration.

Measurements on the prototypeTo test the feasibility of the approach, an 80 W into 8 9 two-switch 4Q flyback subwooferSICAM prototype with average current-mode control was constructed and its photo is shownin Fig. 10. The switching frequency is set to f8 = 15,0 kHz. The prototype resembles thestructure shown in Fig. 8 and it incorporates the aforementioned integrated magnetics forderiving all the auxiliary voltages on the secondary side, as in Fig. 9.Fig. 11 shows in detail the operation of the 4Q flyback SICAM with zero reference. Theshort on-periods of the primary side switches represent some minimum allowed on-timebeing intentionally inserted even with no error voltage on the input of the controller, justto avoid zero-crossing distortion of the output voltage. The state of the one-bit quantizer Qdetermines the secondary side bidirectional switch, which will be turned on right after theprimary side switches seize conducting. The selected bidirectional switch is turned on forthe rest of the time until the primary side switches conduct again, although the state of theone-bit quantizer Q maybe has changed in the meantime. Due to the fast outer voltage loopeven this small ripple in the output voltage is sensed and is causing an immediate changein the control voltage sign, so that the selected bidirectional output switch alternates eachperiod to yield minimum ripple voltage. Making the outer voltage loop slow will cause theoutput voltage ripple to be large, since the guaranteed minimum inductor current with thesaune output switch turned on during few periods will continue charging the output capacitorto large values.Fig. 12 shows the operation of the 4Q flyback SICAM at output power of Po=50 W with200 Hz reference voltage.The efficiency of the prototype is given in Fig, 13, This particular realization of the 4Qflyback SICAM does not have very high efficiency, but this is likely to be improved in thenext prototype.The presented results prove the feasibility of the 4Q flyback SICAM for audio power ampli-fication. Its application is intended for lower power levels and lower audio frequency range,predominantly subwoofer applications.

ConclusionIn this paper, a 4Q flyback converter for direct audio power amplification with uniqueoperation principle has been presented. It is also shown how peak and average currentmode control can be utilized to improve converter performance. New integrated magnetics isproposed for the 4Q flyback SICAM, which fits both the main and the auxiliary transformerson the same magnetic core. The experience gained from the prototype proved that this compactpower conversion topology has the bencfits of being simple and having satisfactory efficiencycombined with reduced volume, high power density, low component count and subsequentlylow cost, which makes it appealing for the low-power and low-end audio power amplifiers.

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Fig. 10 4Q flyback SICAM prototype

Tek JL. Stop M Pos: 0U00D TRIGGER

Typo

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* Mode* r Z E

Coupling

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Fig, 12 Waveforms at P0=50 W with200 Hz refelence: 1) ref. voltage Vref

2) output voltage v^, 3) comparator Qoutput, 4) primar gate diive

Tbk Stop H Poes: UI.IIs TRIGGER

i 1 Types+~~~~~~~~~~~ ~~~SourceMode

*

=

Coupling

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Fig. 11 Wavefotms with zero reference:1) ref. voltage ur rr 2) output voltage v,.

3) coiparator Q output, 4) primary gatedrive

0

a)0

100

90

80

7060

50

40

30

20

10

0-0

Fig. 13SICAM

20 40 60 @0

Output power P0[W]

Efficiency of the 4Q flyback

References[1]. P. Ljuiaev and M. Andersen,iiApproaches building single-stage ac/ac coiversion switch-mode audio power amplifters,"

in Pc. 11th Internationiar Ponver Electronics and Motion Contro/ conferencef EPE-PEMWC 2004, (Riga. Latvia).September 2-4 2004.

[2]. P. Ljtuge and M. Andersen, "Safe-commutation principle for direct single-phase ac-ac converters for uL se in auLdio powerampliicarion;, in Proc. Nordic TWorkstop on Power and Industrial Electronics NORPIE 2004, (Trondlieim, Norvay),June t4-16 204.

[3]. K. Nielsen and L. M. Fenoeio '1i'he ative ptulse modulated transduLcer (at) a novel auidio power conversion systemarchitecture, in 115th Convertion of th Aucdio Engineering Society, AES Proceeditgs. OcLober 10-13 2003. Prepwint5866.

[4]. R. WV Ericlson and D. Maksiniovi6, Fundamentals of Power Electronics. luwer Academic Pubihshers, 2001. Secondedition.

[5]. L. H. Dixon, "Control loop cookbook;, Tech. Rep. SLUPI 13, Unirode Power SLpply Design Seminar SEMI 1CO, 1996.[6]. D. Dala, "A unique four quadrant flyback convener," Tech. Rep. SLUPi 16, Unimrde Powve-r Supply Design Seminar

SENI200, 1997.[71] L. Hr Dixon, 'Average cun-ent inoce coitrol of switc-lhig power supptiesT" Tech. Rep. SLUP09I, Unitroce Power

Supply Designi Seminar SEM700, 1990.

EPE 20)5 - Duroden ISBN:P.10

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